Maximum Likelihood Estimation for the Parameters of New Mixture Maxwell–Boltzmann Distribution and Its Applications

This article introduces a new mixture extension of the Maxwell–Boltzmann distribution (MBD) to enhance data modeling flexibility. Maximum Likelihood Estimation (MLE) is employed to estimate parameters, and key statistical properties are analyzed. In addition, simulation studies are conducted to compare the bias, mean square error, and variance of the estimates over a wide range of sample sizes from n = 5 to 10,000. The new distribution is applied to a real-world heart attack survival dataset to demonstrate its potential in practical applications. These findings highlight the potential of the proposed distribution in survival studies and modeling right-skewed data.